yeah you need the screens backlights attached at least, analogue stick etc are fine to be left disconnected while working on it, i usually just plug the screens back in for testing though so you can make sure its properly working, in regards to all the nand-x, and jrunner stuff....its really not necessary, a SD reader is perfect for the job, i doubt there would be any real difference in speed compared to just using a SD reader, plus its easier to just make the SD adapter so you can use whatever computer you like with no need to have any extra devices handy
SD reader + win32diskimager = happy nand dumping, even with only 1 dat line attatched your still only looking at like 10 mins writing time max taking into account the extra nand size on the n3DS, on the normal 3DS its like 5/6 mins, if you hooked up all 4 dat lines it would be like 5 mins for n3ds, 1-2 mins for standard 3ds's